In the oil and gas industry, geophysical prospecting techniques are commonly used to aid in the search for and evaluation of subterranean hydrocarbon deposits. Generally, a seismic energy source is used to generate a seismic signal which propagates into the earth and is at least partially reflected by subsurface seismic reflectors (i.e., interfaces between underground formations having different acoustic impedances). The reflections are recorded by seismic detectors located at or near the surface of the earth, in a body of water, or at known depths in boreholes. The resulting seismic data may be processed to yield information relating to the location of the subsurface reflectors and the physical properties of the subsurface formations.
Recorded data is a combination of source wavelet and earth properties. The ultimate goal of seismic data processing is to interpret earth properties without the complication of the source wavelet. Reflectivities, including ‘Amplitude Variation with Offset’ or angle parameters (AVO), characterize earth properties and can also be used as input to other prestack inversion algorithms. At the same time, the source wavelet is useful for a variety of seismic processing algorithms, including: (a) phase correction of seismic data, (b) wavelet shaping and deconvolution of seismic data, (c) offset-dependent tuning correction, (d) forward modeling of seismic data and (e) free-surface multiple elimination.
Amplitude variation with angle/offset (AVA/AVO) is the variation in the amplitude of a seismic reflection with the angle of incidence or source-geophone distance. The variation depends on changes in velocity, density, and Poisson's ratio. It is often used as a hydrocarbon gas indicator because gas generally decreases Poisson's ratio and often increases amplitude with incident angle/offset. Other conditions can produce similar effects. The amplitude of an event is often plotted against sin2 θ or (sin2 x), where θ is incidence angle (and x is offset), and the slope or gradient of a best-fit line is measured as the indicator:A(θ)=A 30 B sin2 θ.
Because measurements have to be made with prestack data, the noise level is usually large. The gradient is often determined by the ratios of amplitudes of large-offset to short-offset stacks. Different types of reservoirs have different responses to seismic energy impinging on reservoir surfaces, and these are separated into classes. Amplitude versus angle/offset Class 1 reservoirs have higher impedance than the surrounding rocks, class 2 are those with very small, either positive or negative, impedance contrast, and class 3 are low-impedance reservoirs. In Tertiary clastic sections, class 1 reservoirs often yield dim spots, class 3 bright spots, and class 2 reservoirs are difficult to see unless they have appreciable increase of amplitude with offset. Class 4 reservoirs are low-impedance reservoirs where the magnitude of the response decreases with offset (Rutherford and Williams, 1989).
The effective source wavelet is difficult to measure in practice. The effective source wavelet can be influenced by near-surface structure in the vicinity of the source. Moreover, separation of source and reflectivity via inversion is inherently ill-determined. In a strict mathematical sense it is indeterminate from poststack data alone. Non-parallel moveout information in prestack data, however, provides some degree of leverage to distinguish between source wavelet and reflectivity via prestack inversion. Moveout is the difference in arrival times due to source-to-receiver distance differences.
Prior art methods to estimate the source wavelet and reflectivity can be broadly classified into four approaches. These four approaches are: 1) source wavelet and reflectivity separation using statistically based assumptions, 2) extraction using known reflectivities, 3) inversion/extraction using a known source wavelet, and 4) simultaneous inversion for source and reflectivity. The first three can be applied to either poststack or prestack data and only the fourth method is specific to prestack data.
Separation of source wavelet and reflectivity based on statistical assumptions constrain what would otherwise be an indeterminate problem. The most widely used method is spiking deconvolution where reflectivity is considered to be white and the source is assumed to be minimum phase (Robinson, 1967). Other statistical methods include a 4th-order cumulant approach (Lazear, 1984), the maximum entropy method (Lines and Ulrych, 1977) and homomorphic deconvolution (Ulrych, 1971).
Extraction of source wavelet given known reflectivities is a class of methods that are linear and well-determined in a mathematical sense. The most widely used approach first obtains reflectivities from well logs. Other approaches obtain reflectivities by assuming that certain bright events in seismic data correspond to simple, sharp reflecting interfaces (Buland and More, 2001; Nyman et al., 1996). With either approach the wavelet is then extracted by relating the seismic data with the known reflectivities.
Inversion for reflectivity given a known source wavelet is a less well-determined approach because the bandwidth of seismic data is always less than the bandwidth of the desired reflectivities. One of the common prior art methods is sparse spike inversion using an L1-Norm to extend the bandwidth of the output reflectivity sequence (Oldenburg et al, 1983). Other methods in this class include nonlinear inversion for reflectivity by sparse parameterization and global optimization (Pedersen et al., 1991).
Bill Symes and other researchers at Rice University introduced the concept of simultaneous inversion to separate source and reflectivity based on non-parallel moveout in prestack data, and have given mathematical proofs-of-concept under simple conditions. Prior art studies using the non-parallel moveout concept have obtained mixed results; sometimes the results demonstrated difficulties in convergence (Minkoff and Symes, 1995; Winslow et al., 2000).
There is a need for a fast and efficient method of inverting for source and AVO parameters that quickly leads to an acceptable and stable solution. The present invention satisfies this need.
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